Hurray! I will have my camera for my trip so I can share underwater photos with you folks.

I took the Olympus TG-2 to a specialty battery store and they checked and determined that the battery was fully charged. Then he put it back in and pressed the power button and it came to life for the first time. I can get it on now myself doing the same thing I've done dozens of time since last night trying to get this to work.

The charging indicator still doesn't come on, however, when I plug it in. Perhaps because the battery is fully charged. Time will tell. But at least I will have the camera for my trip. Hopefully, this remaining issue will work itself out. Perhaps it is misunderstanding or the instructions on my part.